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arXiv · 2403.05526

On Koebe radius and coefficients estimate for univalent harmonic mappings

Mikhail Borovikov
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Abstract

The problem on estimate of the Koebe radius for univalent harmonic mappings of the unit disk $\mathbb D=\{z\in\mathbb C : |z|<1\}$ is considered. For a subclass of harmonic mappings with the standard normalization and a certain growth estimate for analytic dilatation, we provide new estimate for the Koebe radius. New estimate for Taylor coefficients of the holomorphic part of a function from the subclass under consideration is obtained as a corollary.

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Mikhail Borovikov. 2024-03-08. On Koebe radius and coefficients estimate for univalent harmonic mappings. https://arxiv.org/abs/2403.05526

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